@misc{CollierHauer, author = {Collier, Timothy Allen and Hauer, Daniel}, title = {A density result for doubly nonlinear operators in L1}, series = {Discrete and Continuous Dynamical Systems - S}, volume = {17}, journal = {Discrete and Continuous Dynamical Systems - S}, number = {4}, publisher = {American Institute of Mathematical Sciences (AIMS)}, issn = {1937-1632}, doi = {10.3934/dcdss.2024031}, pages = {1663 -- 1671}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Analysis}, edition = {2}, publisher = {Springer Berlin Heidelberg}, address = {Berlin, Heidelberg}, isbn = {978-3-662-69864-8}, doi = {10.1007/978-3-662-69865-5}, pages = {625}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Minimal graphs in Riemannian spaces}, series = {Calculus of Variations and Partial Differential Equations}, volume = {63}, journal = {Calculus of Variations and Partial Differential Equations}, number = {5}, issn = {1432-0835}, doi = {10.1007/s00526-024-02704-w}, pages = {1 -- 47}, language = {en} } @misc{GurkaHauer, author = {Gurka, Petr and Hauer, Daniel}, title = {More insights into the Trudinger-Moser inequality with monomial weight}, series = {Calculus of Variations and Partial Differential Equations}, volume = {60}, journal = {Calculus of Variations and Partial Differential Equations}, publisher = {Springer Science and Business Media LLC}, issn = {0944-2669}, doi = {10.1007/s00526-020-01890-7}, pages = {27}, language = {en} } @misc{Hauer, author = {Hauer, Daniel}, title = {Regularizing effect of homogeneous evolution equations with perturbation}, series = {Nonlinear Analysis}, volume = {206}, journal = {Nonlinear Analysis}, publisher = {Elsevier BV}, issn = {0362-546X}, doi = {10.1016/j.na.2021.112245}, pages = {34}, language = {en} } @misc{AndrewsClutterbuckHauer, author = {Andrews, Ben and Clutterbuck, Julie and Hauer, Daniel}, title = {The fundamental gap for a one-dimensional Schr{\"o}dinger operator with Robin boundary conditions}, series = {Proceedings of the American Mathematical Society}, volume = {149}, journal = {Proceedings of the American Mathematical Society}, number = {4}, publisher = {American Mathematical Society (AMS)}, issn = {0002-9939}, doi = {10.1090/proc/15140}, pages = {1481 -- 1493}, language = {en} } @misc{AndrewsClutterbuckHauer, author = {Andrews, Ben and Clutterbuck, Julie and Hauer, Daniel}, title = {Non-concavity of the Robin ground state}, series = {Cambridge Journal of Mathematics}, volume = {8}, journal = {Cambridge Journal of Mathematics}, number = {2}, publisher = {International Press of Boston}, issn = {2168-0930}, doi = {10.4310/cjm.2020.v8.n2.a1}, pages = {243 -- 310}, language = {en} } @misc{ArendtHauer, author = {Arendt, Wolfgang and Hauer, Daniel}, title = {Maximal L2-regularity in nonlinear gradientsystems and perturbations of sublinear growth}, series = {Pure and Applied Analysis}, volume = {2}, journal = {Pure and Applied Analysis}, number = {1}, publisher = {Mathematical Sciences Publishers}, issn = {2578-5885}, doi = {10.2140/paa.2020.2.23}, pages = {23 -- 34}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Spektraltheorie selbstadjungierter Operatoren im Hilbertraum und elliptischer Differentialoperatoren}, publisher = {Springer Spektrum}, address = {Heidelberg [u.a]}, isbn = {978-3-662-58069-1}, doi = {10.1007/978-3-662-58069-1}, pages = {xi, 259}, language = {de} } @article{HauerHeLiu, author = {Hauer, Daniel and He, Yuhan and Liu, Dehui}, title = {Fractional Powers of Monotone Operators in Hilbert Spaces}, series = {Advanced Nonlinear Studies}, volume = {19}, journal = {Advanced Nonlinear Studies}, number = {4}, publisher = {Walter de Gruyter GmbH}, issn = {1536-1365}, doi = {10.1515/ans-2019-2053}, pages = {717 -- 755}, abstract = {The aim of this article is to provide a functional analytical framework for defining the fractional powers As for -1 < s < 1 of maximal monotone (possibly multivalued and nonlinear) operators A in Hilbert spaces.We investigate the semigroup {e-As t}t≥0 generated by -As, prove comparison principles and interpolations properties of {e-As t}t≥0 in Lebesgue and Orlicz spaces. We give sufficient conditions implying that As has a sub-differential structure. These results extend earlier ones obtained in the case s = 1/2 for maximal monotone operators [H. Br{\´e}zis, {\´E}quations d'{\´e}volution du second ordre associ{\´e}es {\`a} des op{\´e}rateurs monotones, Israel J. Math. 12 (1972), 51-60], [V. Barbu, A class of boundary problems for second order abstract differential equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 19 (1972), 295-319], [V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff international, Leiden, 1976], [E. I. Poffald and S. Reich, An incomplete Cauchy problem, J. Math. Anal. Appl. 113 (1986), no. 2, 514-543], and the recent advances for linear operators A obtained in [L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations 32 (2007), no. 7-9, 1245-1260], [P. R. Stinga and J. L. Torrea, Extension problem and Harnack's inequality for some fractional operators, Comm. Partial Differential Equations 35 (2010), no. 11, 2092-2122].}, language = {en} }